4 - Structural Optimization of Offshore Wind Turbines - Petrini

Structural Optimization of Offshore Wind Turbines
Mario Torcinaro, Francesco Petrini, Stefania Arangio
francesco.petrini@uniroma1.it
Department of Structural and Geotechnical Engineering
Sapienza University of Rome

MotivationsEARTH&SPACE 2010
2 Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.itEARTH&SPACE 2010
Motivations
1. Offshore wind farms are relatively new structural facilities located in
challenging environment, the preliminary design of the structural elements is
usually very conservative. A refinement is needed.
2. An offshore wind farm is formed by a number of wind turbines (50-200
elements) and, consequently, a small individual reduction of structural
material amount can lead to significant saving of money if regarding the
whole farm.
3. A new support structure is proposed here, and the correct sizing of its
structural parts is crucial in this phase.

EARTH&SPACE 2010
INTRODUCTION
System design approach for
complex structural systems
optimization
Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.itEARTH&SPACE 2010

z
y
x,x’
z’
y’
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
z
y
x,x’
z’
y’
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
d
Complex system
3 EARTH&SPACE 2010
Introduction Part I Part II
A “Complex System”

z
y
x,x’
z’
y’
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
z
y
x,x’
z’
y’
Waves
Mean
wind
Current
P
(t)vP
(t)w P
(t)uP
Turbulent
wind Vm(zP)
P
H
h
vw(z’)
Vcur(z’)
d
3 EARTH&SPACE 2010
A “Complex System”
NonLinearities
Uncertainty
Interactions
Complex system

System Engineering
4 Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.it
A System Engineering Approach
Since the structural behavior of offshore wind turbines is influenced by nonlinearities,
uncertainties or interactions, they can be defined as complex structural system
“a set of interrelated components which interact one with another
in an organized fashion toward a common purpose” (NASA,
1995)
Structure Structural system
“a device to channeling loads”
Decomposition
Structure
Actions
Performances
Structural
System
A fundamental task concerns the Structural System and Structural Performance
decomposition
EARTH&SPACE 2010
Bontempi F., Li H., Petrini F., Gkoumas K., (2008). Basis of Design of Offshore Wind Turbines by System Decomposition,
Proceedings of the ASEM'08, Jeju , Korea, 26-28 May 2008.

System Engineering
5 Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.it
Structural decomposition
EARTH&SPACE 2010
Macro - LevelDetail - Level
Structure
decomposition
Main
structure
(carrying loads)
Secondary
structure
Auxiliary
structure
Rotor-nacelle
assembly
Support
structure
Energy
production
Energy transfer
Operation
Maintenance
Emergency
Substructure
Tower
Rotor
Nacelle
Blades
Foundations
Meso - Level
Junctions
Junctions
Micro - Level
Bontempi F., Li H., Petrini F., Gkoumas K., (2008). Basis of Design of Offshore Wind Turbines by System Decomposition,
Proceedings of the ASEM'08, Jeju , Korea, 26-28 May 2008.

Optimization in design process
6 EARTH&SPACE 2010
Structural design and structural optimization
Topological
Optimization
Design
Optimization
Structural check
Best design
config?
Refine
No
STOP
PBD
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
Yes

7 EARTH&SPACE 2010
Structural design and structural optimization
Topological
Optimization
Design
Optimization
PBD
No
Structural check
Best design
config?
Refine
STOP
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
Refinement of the design
configuration with the goal of
obtaining satisfaction
performances in economical way
Shape optimization
(Options definition)
Parameters optimization
(Options refinement)
Feasible configuration selection
(Option selection)
Yes
Optimization in design process
Present Work

EARTH&SPACE 2010
PART I, Case study structure:
Modeling and Optimization
aspects

Support Structures
9 EARTH&SPACE 2010
Typologies of support structures
Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore wind
turbines. Report for MTC OTC Project
Water depth (m) Foundation type
0-10 Gravity based
0-30 Mono-pile
>20 Tripod/Jacket
>50 Floating
Bontempi, F. (2010). Advanced
topics for offshore wind turbines.
Earth&Space 2010 Conference
Strutted Quadruped

Objective
Funcrion
Analytics
10 EARTH&SPACE 2010
Optimization problem formulation
Unconstrained Design
spaceConstrains
Constrained Design space
We must find the minimum of a certain Objective Function f, depending on certain Design
Variables (DV) x1,…,xn subjected to a number of constrains and by bounding the values of
a certain number of state variables (SV)
nn11
n
LSV,,LSV,RXx,0)x(g,0)x(hbeing)x(fmin  
Constrains Design variables State variables
Objective
Functions
Von Mises
stresses

11 EARTH&SPACE 2010
First order Optimization method
One introduces the following unconstrained objective function:
         





  
 
2 31 m
1i
m
1i
iwih
m
1i
ig
n
1i
ix
0
wPhPgPqxPq,Q
f
f
x
 
λ2
ii
i
ig
αg
g
gP 







λ is a large integer so that the function will be very large when the constraint is
violated and very small when it is not
Q is the dimensionless unconstrained objective function,
Px is the exterior penalty functions applied to the design variables,
Pg, Ph, and Pw are penalties applied to the constrained design and state variables,
f0 is the reference objective function value that is selected from the current group of design sets
q is the response surface parameter .
For each optimization iteration (j) a search direction vector d(j) is devised. The next iteration (j+1) is obtained
from the following equation:
     j
j
j1j
s dxx 
   
   1j
1jk
jj
rq,Q 
 dxd
 
   
    
 
 
  21j
jT1jj
1j
q,Q
q,Qq,Qq,Q
r






x
xxx
where sj is the line search parameter, and
The key to the solution of the global minimization of Q relies on the sequential generation of the search directions
and on internal adjustments of the response surface parameter (q).
ANSYS Inc. (2008). ANSYS Theory reference
Analytics

12 EARTH&SPACE 2010
Optimization problem algorithm
Algorithm

Modeling
13 EARTH&SPACE 2010
Structural
system
modeling
Structure
Actions
Interactions
Modeling
levels
Systemic
Macro
Meso
Micro
Model
level
Scale Detail level Type of Finite Elements
Systemic
level
wind farm
approximate shape of the structural
components
BEAM elements
Macro
level
single turbine
approximate shape of the structural
components, correct geometrical
ratios between the components
BEAM elements
Meso
level
single turbine
detailed shape of the structural
components
SHELL, BRICK elements
micro
level
individual components
detailed shape of the connecting
parts
SHELL, BRICK elements
Differentiation of the modeling levels
Bontempi F., Li H., Petrini F., Manenti S., (2008). Numerical modeling for the analysis and design of offshore wind turbines,
Proceedings of ASEM'08, Jeju, Korea, 26-28 May 2008

1°1°
Macro
Global response
Meso Micro
Levels of modeling and results detail level
Jacket - Tower
connection
Detailed global response and
medium-detailed local
response
Detailed local response and
analysis of connections
ModelingIntroduction Part I Part II
14 EARTH&SPACE 2010 Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.itEARTH&SPACE 2010

EARTH&SPACE 2010
PART II, Case study structure:
Problem definition and results

Design variables
15 EARTH&SPACE 2010
Application
x1
x2
• Structure and piles 180 m
• Structure height: 140 m
• Immersed: 35 m
• Over water level: 105 m
Local constraints:
•maximum Von Mises ideal stress equals
to 300MPa (strength criterion);
•maximum compression stress equals to
200MPa (local instability criterion);
•maximum ratio diameter/thickness
equals to 100 (local instability criterion);
Global constraints:
•Eulerian buckling multiplier greater that 5;
•maximum horizontal displacement
permitted 4 m.
• Objective Function: TOTAL VOLUME

Results
16 EARTH&SPACE 2010
Macro-level model: Design variables trend
Diameters Thicknesses

17 EARTH&SPACE 2010
Macro-level model: State variables trend
Compression stresses
Von Mises stresses
Results

18 EARTH&SPACE 2010
Macro-level model: Configuration evolution
Results

19 EARTH&SPACE 2010
Macro-level model: Objective function
Results

20 EARTH&SPACE 2010
Meso-level model
Results

21 EARTH&SPACE 2010
Meso-level model: Effective buckling modes detection
Macro-level model Meso-level model
Results
1° buckling mode load multipler = 9,08
1° buckling mode load
multipler = 10,12

Optimal configuration
Optimal ConfigIntroduction Part I Part II
VOLUME=116 [m3]
Diamet ers[m] Thicknesses[m] d/t
D1 2.25 T1 3.1E-02 72.5
D2 3.14 T2 4.2E-02 75.5
D3 4.03 T3 4.2E-02 96.9
D4 4.56 T4 4.2E-02 109.5
D5 5.09 T5 5.2E-02 97.5
D6 2.37 T6 3.3E-02 71.8
D7 5.09 T7 5.2E-02 97.5
D8 5.30 T8 5.4E-02 98.3
D9 5.05 T9 5.4E-02 93.7
D10 4.80 T10 5.4E-02 89.1
D11 4.55 T11 5.4E-02 84.5
D12 4.31 T12 4.4E-02 97.9
D13 3.84 T13 4.4E-02 87.3
D14 3.37 T14 4.4E-02 76.7
D15 2.91 T15 4.4E-02 66.0
D16 2.44 T16 3.8E-02 64.8
D17 1.52 T17 1.6E-02 95.9
D18 2.32 T18 2.3E-02 99.4

Monopile-Quadruped comparison
Quadruped:
 VOLUME = 116 [m3]
 Weight = 904 [t]
 D max = 5 [m]
Monopile:
 VOLUME = 234 [m3]
 Weight = 2377 [t]
 D max = 9 [m]
Optimal ConfigIntroduction Part I Part II

EARTH&SPACE 2010
24 Structural Offshore Wind Turbines Optimization francesco.petrini@uniroma1.itEARTH&SPACE 2010
Conclusions
1. The Design Optimization of Owts is a fundamental step in the design of
Offshore Wind Farms.
2. The Design Optimization of such a complex structural systems has been
carried out by assuming simplified models for the actions.
3. Multi level detail models are needed in order to capture the main physical
aspects.
4. A new support structure is proposed here, the optimization produced good
results in terms of weight if compared with another feasible solution (a
monopile support structure).

4 - Structural Optimization of Offshore Wind Turbines - Petrini

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